KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION


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1 KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 F PERIODIC TEST III EXAM ( ) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit Total Number system Number Systems 1(1) 2(1) 3(1)* 4(1) 10(4) 10(4) Algebra Polynomials 1(1) 2(1) 3(1) 4(1)* 10(4) Linear Equations in two variables 1(1)  3(1) 4(1) 8(3) 18(7) Coordinate Coordinate (1) 4(1) 4(1) Introduction to Euclid s (1)  3(1) Lines and Angles (1)*  3(1) Triangles (1)*  3(1) Quadrilaterals  2(1)  4(1) 6(2) Area of Parallelograms and triangles  2(1) 3(1)*  5(2) Circles 1(1)  3(1) 4(1)* 8(3) Constructions (1) 4(1) 32(11) Mensuration Heron s Formula 1(1) 2(1) 3(1)  6(3) Surface Areas and Volumes 1(1) 2(1) 3(1) 4(1)* 10(4) 16(7) Total 6(6) 12(6) 30(10) 32(8) 80(30) 80(30) Note: *  Internal Choice Questions Prepared by: M. S. KumarSwamy, TGT(Maths) Page  1 
2 KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 F PERIODIC TEST III EXAM ( ) SUBJECT: MATHEMATICS MAX. MARKS : 80 CLASS : IX DURATION : 3 HRS General Instruction: (i) All questions are compulsory. (ii) This question paper contains 30 questions divided into four Sections A, B, C and D. (iii) Section A comprises of 6 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 10 questions of 3 marks each and Section D comprises of 8 questions of 4 marks each. (iv) There is no overall choice. However, an internal choice has been provided in four questions of 3 marks each and three questions of 4 marks each. You have to attempt only one of the alternatives in all such questions. (v) Use of Calculators is not permitted SECTION A Questions 1 to 6 carry 1 mark each. 1. What is the total surface area of a hemisphere of base radius 7cm? 2. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k. 3. The height of an equilateral triangle measures 9 3 cm. Find its area. 4. Without actually calculating, find the value of (25) 3 (75) 3 + (50) Simplify: In the Fig, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If DBC = 60 and BAC = 30, find BCD. SECTION B Questions 6 to 12 carry 2 marks each. 7. A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume of the solid so formed. p 8. Show that can be expressed in the form of, where p and q are integers and q q Factorise: x x x 10. The angle between two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is Find the angles of the parallelogram. Prepared by: M. S. KumarSwamy, TGT(Maths) Page  2 
3 11. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle. 12. In the below figure, ABCD is a parallelogram; AB = 10 cm; BM = 8 cm and DL = 6 cm, then find AD. D C M A L SECTION C Questions 13 to 22 carry 3 marks each. 13. In the below fig. ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersects DC at P, show that ar( BPC ar DPQ ) B In the below figure, ABCDE is any pentagon. BP drawn parallel to AC meets DC produced at P and EQ drawn parallel to AD meets CD produced at Q. Prove that ar (ABCDE) = ar (APQ) 14. Line l is the bisector of an angle A and B is any point on l. BP and BQ are perpendiculars from B to the arms of A (see the below figure). Show that: (i) APB AQB (ii) BP = BQ or B is equidistant from the arms of A. AB is a line segment and P is its midpoint. D and E are points on the same side of AB such that BAD = ABE and EPA = DPB (see the above right sided figure). Show that (i) DAP EBP (ii) AD = BE Prepared by: M. S. KumarSwamy, TGT(Maths) Page  3 
4 15. In the adjoining figure you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade. 16. Find the area of the trapezium PQRS with height PQ given in the above right sided Figure 17. Verify: (i) x 3 + y 3 = (x + y) (x 2 xy + y 2 ) (ii) x 3 y 3 = (x y) (x 2 + xy + y 2 ) 18. In the adjoining figure, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB CD. In the above right sided figure, the side QR of PQR is produced to a point S. If the bisectors of PQR and PRS meet at point T, then prove that QTR = 1 2 QPR. 19. In the Fig., if 1 = 3, 2 = 4 and 3 = 4, write the relation between 1 and 2, using an Euclid s axiom. 20. Give the geometric representations of 2x + 9 = 0 as an equation (i) in one variable (ii) in two variables. Prepared by: M. S. KumarSwamy, TGT(Maths) Page  4 
5 21. Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle. 22. Find the value of a and b in 2 3 a b Simplify by rationalizing the denominator SECTION D Questions 23 to 30 carry 4 marks each. 23. AC and BD are chords of a circle which bisect each other. Prove that (i) AC and BD are diameters, (ii) ABCD is a rectangle. Bisectors of angles A, B and C of a triangles ABC intersect its circumcircle at D, E and F respectively. Prove that the angles of DEF are A, B and C 24. A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m. (i) How many students can sit in the tent if a student, on an average, occupies 5 7 m2 on the ground? (ii) Find the volume of the cone. Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm 20 cm 5 cm and the smaller of dimensions 15 cm 12 cm 5 cm. For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind. 25. Construct a triangle ABC, in which B = 60, C = 45 and AB + BC + CA = 11 cm. 26. Represent the real number 2, 3, 5 on a single number line. 27. P, Q, R and S are respectively the midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC BD. Prove that PQRS is a rectangle. 28. Plot the following points and write the name of the figure thus obtained : P( 3, 2), Q ( 7, 3), R (6, 3), S (2, 2) 29. Draw the graph of the linear equation 2x + 3y = 12. At what points, the graph of the equation cuts the xaxis and the yaxis? 30. Find the values of a and b so that the polynomial x 3 10x 2 +ax + b is exactly divisible by (x 1) as well as (x 2). Without actual division, prove that 2x 4 5x 3 + 2x 2 x + 2 is divisible by x 2 3x + 2. Prepared by: M. S. KumarSwamy, TGT(Maths) Page  5 
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